Inversely proportional
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When prices are getting higher, you will get less products with the same amount of money as earlier. It is said that purchasing power decreases. Prices and purchasing power are inversally proportional to each other.
- You will get only half of items with the same amount of money, if they cost twice as much as now.
The more of x the less of y.Mathematical equation for inverse variation can be written as
Example 1.
You bought 10 items for 50 euros in sale. When the sale was over, you had to buy these items more. You found, that the original unit price was double compared to the price in the sales. How many items did you get?
At sales, , where in the unknown unit price. Obviously, the unit price euros. The original unit price must be 10 euros meaning that you can only get 5 items with 50 euros.
If you want to solve this with inverse variation, the ratio
must be satisfied all the time.
In this case,
where y is number of the items bought at original unit price.
Example 2.
If a group works 7 hours a day, a job can be done in 25 days. If they have only 20 days to do the job, how many hours more should they work during a day?
In this example, the job remains the same. The less days they have for doing it, the more hours a day they should work. In fact, the hours needed for a job is constant. Mathematically,
Thus, they should work 1 hour 45 minutes longer every day.